CommunityModularity

As of Version 10, all the functionality of the GraphUtilities package is built into the Wolfram System. »

CommunityModularity[g,partition]

gives the community modularity of a partition.

CommunityModularity[g,assignment]

gives the community modularity of an assignment.

Details and Options

CommunityModularity functionality is now available in the built-in Wolfram Language function GraphAssortativity.
To use CommunityModularity, you first need to load the Graph Utilities Package using Needs["GraphUtilities`"].
A community in a network is a group of vertices such that there is a higher density of edges within the group than between them.
Given a graph , let the vertex set be partitioned into subsets such that each subset belongs to one community. The community modularity of this partition is defined as , where is the percentage of edges that have both ends in community , and is the percentage of edges that start from community . In other words, and .
The community modularity is a number less than or equal to 1. A large positive value indicates that the vertex partition gives significant community structure.
The following option can be given:
Weighted False whether edges with higher weights are preferred during matching